Modern spectroscopy techniques can yield data including spectral image information in multiple spatial, temporal, and other experimental dimensions. Exemplary data can include tens of thousands of images or spectra for a single chemical sample. Understanding the chemical or physical phenomenon underlying such data can be challenging. Thus, a remaining challenge is the ability to reduce vast quantities of data into meaningful chemical information, such as the presence or absence of particular chemical bonds, atoms, charge, etc., while maintaining important dimensional information.
Various methods simplify the analysis but have limitations. For instance, one technique to simplify data is to analyze a single mean spectrum (e.g., a mean spectrum that includes a mean average of intensity data for over 10,000 spectra). This technique reduces the data into a single spectrum but at the cost of removing other valuable information, such as spatial locations of a particular chemical species, time-dependent changes of a concentration of a particular chemical species, etc. In another instance, complex chemical interactions are conventionally modeled and solved in a linear manner. This simplification may incorrectly explain such interactions, as many chemical reactions are best explained (in whole or in part) by non-linear mechanisms. Accordingly, additional methods are desired that facilitate expeditious analysis of complicated data while maintaining the data set and/or accommodating non-linear phenomenon.